On the Interpretation of Anaphoric Noun Phrases: Towards a Full Understanding of Partial Matches Emiel Krahmer IPO, Eindhoven
&
Kees van Deemter ITRI, Brighton
Abstract Starting from the assumption that NPs of all kinds can be anaphoric on antecedents in the linguistic context, we work towards a general theory of context-dependent NP meaning. Two complicating factors are that the relation between anaphors and antecedents is by no means unrestricted and that often there is a partial match between anaphor and antecedent. We argue that the presuppositions-as-anaphors approach of van der Sandt provides a natural starting point for our enterprise. Unfortunately, this theory has a number of deficiencies for our purposes, in particular where the treatment of partial matches is concerned. We propose a number of modifications of van der Sandt’s formal theory and apply the modified algorithm first to definite NPs and later to NPs of all kinds. The resulting modified version of the presuppositions-asanaphors theory is argued to be more general, formally more precise, and empirically more adequate than its predecessor.
1
I NTRODUCTION
In this article we work towards a general theory of context dependent Noun Phrase (NP) meaning. Our starting point is the following hypothesis: Hypothesis 1: NPs of all kinds can depend on linguistic context for their interpretation. Theories of anaphora can be used to explain the nature of the dependency. Various authors have pointed out that there is an analogy between anaphors and presuppositions, of which van der Sandt (1992) is probably the most explicit. The crux of van der Sandt’s approach is that, in many respects, presuppositions behave simply as anaphors. A consequence of his presuppositions-as-anaphors view is that the notorious projection problem for presuppositions1 can be reduced to the problem of resolving anaphoric pronouns. We take it that ‘presupposition-hood’, and more specifically the mechanisms which determine whether a presupposition is projected or not, are important factors related to hypothesis 1, and this is reflected by the following hypothesis (to be made more precise below). Hypothesis 2: All NPs with a strong or accented determiner trigger an existence presupposition. To build a sensible theory on such general assumptions, a number of hurdles have to be taken. To begin with, the anaphoric dependency relation that can be seen to hold between two NPs is by no means unrestricted; in certain cases an anaphoric relation between a would-be anaphor and a wouldbe antecedent is impossible due to independent constraints. Another factor which complicates the anaphoric dependency relation is that there often is a partial match between an anaphor and its potential antecedent. 1
Langendoen & Savin (1971: 54): “how [are] the presupposition and assertion of a complex sentence (...) related to the presupposition and assertion of the clauses it contains?”
1
Interestingly, van der Sandt (1992) argues that such partial match examples provide a good illustration of the differences between his presuppositions-as-anaphors approach and its main competitor, the contextual satisfaction approach to presuppositions (Karttunen 1974, Stalnaker 1973, 1974, Heim 1983, 1992, Beaver 1992, 1995). The central idea of this latter approach is that the presuppositions of a sentence must be entailed by the context of interpretation in order for this context to admit the sentence. When van der Sandt (1992: 349-351) compares his approach to the contextual satisfaction approach, he claims that the difference between the two comes out most clearly when considering cases of a partial match, of which (1) is one example (similar examples are discussed in Soames 1982). (1)
If John has an oriental girlfriend, his girlfriend won’t be happy.
Given that his will be bound to John in this example (there is no alternative), the possessive description his girlfriend triggers the presupposition that John has a girlfriend. According to van der Sandt, this example displays a genuine ambiguity between two readings, depending on whether his girlfriend refers to an oriental girlfriend or not. The two readings may be paraphrased as (2.a) and (2.b) respectively. (2)
a.
If John has ani oriental girlfriend, shei won’t be happy.
b. John has aj girlfriend and if he has ani oriental girlfriend (as well), shej won’t be happy. Van der Sandt provides extra evidence for this ambiguity by showing that different continuations can eliminate one of the readings. Thus, continuing (1) with (3) eliminates the (2.a) reading in favor for (2.b). (3)
She has always been rather jealous. (van der Sandt 1992: 351)
On the other hand, continuing (1) with (4) will eliminate the (2.b) paraphrase: (4)
But if he has one from France, ...(van der Sandt 1992: 350)
Van der Sandt claims that this ambiguity of (1) is exactly what his theory predicts, while the satisfaction approach only gets the first reading; after all having an oriental girlfriend entails having a girlfriend. In sum, the presuppositions-as-anaphors approach seems to provide an excellent starting point for our study of the interpretation of anaphoric noun phrases: the approach not only trades on the assumption that presuppositions and anaphors have much in common, but is also the empirically most adequate theory of presuppositions today (Beaver 1996:983) and it has something substantial to say about partial matches as well. Unfortunately, the theory also has a number of deficiencies for our purposes, in particular where the treatment of partial matches is concerned. If we apply van der Sandt’s formal theory to examples such as (1), as we do below, we find that there is a discrepancy between his intuitions about these partial match examples and the predictions made by his formal theory. It turns out that the ambiguity of (1) is not actually predicted by his algorithm and, moreover, that some of the interpretations predicted by it are incorrect. Therefore our current program is as follows. We first sketch the presuppositions-as-anaphors approach (section 2). In section 3, we take a more systematic look at the partial match phenomenon and van der Sandt’s predictions. In section 4 we try to solve some of the problems with van der Sandt’s theory by proposing a number of modifications of the presuppositions-as-anaphors approach and argue that the result yields the desired interpretations. In doing so, we follow a different route from van der Sandt (1992). Initially, we explicitly limit our discussion to presuppositions triggered by definite descriptions (section 4.2). After that, we argue that the presuppositions-as-anaphors 2
paradigm can be applied to a much larger class of NPs. First, we show how our treatment of definite descriptions carries over to other definite NPs. This includes, primarily, the more obvious cases such as possessives, proper names, and pronouns, but we also argue that a couple of the more notorious phenomena in this area (bridging, epithets) present no unresolvable problems for the current approach. Second, and perhaps more speculatively, we show how our modified account allows us to propose a completely general Noun Phrase presupposition scheme that applies to definite as well as non-definite NPs (section 4.4). In the discussion, we discuss some possibilities for future research and illustrate how our modified version of the presuppositions-as-anaphors theory can be viewed as a ‘bridge’ between the proposals in van Deemter (1992) and those in van der Sandt (1989, 1992). This comparison also serves to highlight an important element of the presuppositions-as-anaphors theory, namely its emphasis on a preference order between possible interpretations.
2
VAN
DER
S ANDT ’ S
PRESUPPOSITIONS - AS - ANAPHORS APPROACH
As said, the central tenet of van der Sandt’s (1992) approach is that presuppositions are anaphors. More concretely, he argues that presuppositions can be handled using the same mechanism which resolves anaphoric pronouns in Discourse Representation Theory (DRT, Kamp 1981, Kamp & Reyle 1993). Thus, when a presupposition is encountered we look for a suitable and accessible antecedent to which we can ‘bind’ the presupposition. Consider example sentence (5), discussed by van der Sandt (1992:360/1): (5)
If John has a child, his child is happy.
The possessive definite his child triggers two presuppositions: that there is a male individual, and that this male individual has a child. For the sake of illustration, we assume that the presupposition triggered by the pronoun has been resolved as John. When this has been done, the Discourse Representation Structure (DRS) for example (5) looks as follows: (DRS 1)
x x = john y child(y) poss(x; y)
=)
happy(z) z @ child(z) poss(x; z)
The consequent of the conditional contains an embedded DRS, representing the presupposition that John has a child. We mark a DRS as presuppositional by prefixing it with a @ . The @ operator was introduced in Beaver (1992), but here it is only used to syntactically distinguish presuppositional DRSs from ordinary, assertional ones. Now van der Sandt’s presupposition resolution algorithm is applied to this DRS, and starts looking for a suitable and accessible antecedent. Obviously, the discourse referent introduced for a child (i.e., y ) is the ideal candidate. So, the presupposition can be bound. Binding a presupposition goes as follows: the presuppositional DRS is removed from the DRS where it originates (the source DRS, for short), and merged with another DRS (henceforth the target DRS ), namely the DRS which introduces the antecedent to which the presupposition is bound. Furthermore, this target DRS is extended with an equality condition which equates the referent introduced in the presuppositional DRS with the referent of the antecedent. In this way the anaphor is ‘absorbed’ by the antecedent (van der Sandt 1992:349). As van der Sandt (1992:357) 3
puts it: “In the case of anaphoric binding the resolver puts in equations which link discourse markers and transfer the conditions associated with the anaphoric expression to the binding site”. By binding the presupposition, (DRS 1) is transformed into ( DRS 2) (DRS 2)
x x = john y; z child(y) poss(x; y) child(z) poss(x; z) y=z
=)
happy(z)
It is easily seen that (DRS 2) is equivalent with (DRS 3), which is also the DRS which would be used to represent (6). In fact, the similarity between examples such as (5) and (6) is one of the suggestive facts which van der Sandt discusses to motivate his presuppositions-as-anaphors approach. (DRS 3)
x x = john y child(y) poss(x; y)
(6)
=) happy(y)
If John has a child, it is happy.
A difference between presuppositions and pronouns shows up when there is no suitable and accessible antecedent. In that case, a presupposition can be accommodated. Consider the following example with its associated DRS: (7)
If John has an oriental girlfriend, his son is happy.
(DRS 4)
x x = john y oriental(y) happy(z) girlfriend(y) z =) poss(x; y) @ son(z) poss(x; z)
4
Again, the resolver looks for an accessible and suitable antecedent to bind the presupposition that John has a son. There are two accessible antecedents (John and his oriental girlfriend) but neither can qualify as suitable. Hence we accommodate the presuppositional DRS. If certain conditions (to be discussed below) are met, accommodation takes place in the main DRS (see van der Sandt 1992: 345 for explanation). Technically, accommodating a presuppositional DRS amounts to removing it from the source-DRS and merging it with the target DRS (which —under normal circumstances— is the main DRS). Thus: (DRS 5)
x; z x = john son(z) poss(x; z) y happy(z) oriental(y) = ) girlfriend(y) poss(x; y)
This results in a reading which may be paraphrased as John has a soni and if John has an oriental girlfriend, hei is happy. As this paraphrase indicates, after accommodating the presupposition the resulting DRS entails that John has a son. In general: accommodating the presupposition in the main DRS yields a ‘presupposing’ reading (the presupposition is projected). By contrast, from (DRS 3) it does not follow that John has a child; the presupposition is not projected and this produces a ‘non-presupposing’ reading. An important element of the presuppositions-as-anaphors approach is that the algorithm associates a set of allowed resolutions to a DRS containing presuppositional DRSs. For instance, accommodation can in principle take place in every (sub-)DRS which subordinates the DRS containing the presuppositional DRS. The ‘in principle’ restraint refers to the fact that each instance of accommodation should satisfy a number of independently motivated constraints. One of them is called the Consistency Constraint. This constraint says that accommodating a presupposition must never lead to an inconsistent DRS. Consider: (8)
It is not the case that John is besotted with his oriental girlfriend, because John has no girlfriend.
Accommodating the presupposition that John has an oriental girlfriend in the main DRS (and thus not within the scope of the negation) is easily seen to yield a contradiction. Therefore, global accommodation is ruled out, and the presupposition is accommodated locally (i.e., within the scope of the negation). The resulting reading can be paraphrased as It is not the case that John has an oriental girlfriend which he is besotted with, because John has no girlfriend. Another constraint is the so-called Informativity Constraint, which rules out interpretations that lead to excessive redundancy. Van der Sandt uses this constraint, among other things, to legislate against conditional representations where the information in the antecedent follows from material present in an accessible DRS (e.g., the main one). Thus, consider (9)
If John has children, his children will be spoiled.
Suppose that the presupposition triggered by the children is accomodated in the top of the DRS, thus guaranteeing the existence of John’s children. Then the antecedent DRS of the conditional (John has children) violates the Informativity Constraint because it has become redundant given 5
the accommodated information. As a result, this interpretation is ruled out. For more information on the background and formalization of these constraints we refer to van der Sandt (1992: 367369). So, there may be various ways of resolving a presuppositional DRS, and together all these possibilities form the set of allowed resolutions. This brings us to a last, crucial ingredient of van der Sandt’s theory: the definition of a preference order over permitted interpretations. One could argue that this preference order is what gives the theory content. After all, if all allowed readings were equally preferred, we would get an extremely liberal theory. For example, it would mean that for the following example the accommodation reading (which intuitively is highly non-preferred) would be just as ‘good’ as the obvious binding reading. (10) Whenever a young cat and an old cat fight over a fish bone, the young cat seizes it. Notice incidently that assigning preference orders is fairly common with theories dealing with ambiguities, perhaps most prominently by implementations of theories of anaphora resolution (e.g., Sidner 1979), but also by theories of quantifier scope ambiguities (see e.g., Hobbs and Shieber 1987:48-49 for some discussion). Van der Sandt (1992:345,357) defines a preference order based on the following general principles: D EFINITION 1 (Van der Sandtian preferences) 1. Binding to a suitable antecedent is preferred over accommodation. 2. Accommodation is preferred to occur as ‘high’ (far away from the source-DRS) as possible. 3. Binding is preferred to occur as ‘low’ (near the source-DRS) as possible. In most cases, these three preference rules order the set of admissable resolutions in such a way that there is one most preferred reading. For example, even though intuitively sentence (7) is not ambiguous, it is predicted to have three different interpretations: one obtained by global accommodation (DRS 5), one obtained by intermediate accommodation (where the target DRS is the antecedent DRS of the implicational condition), and one obtained by local accommodation (the target and source DRS are one and the same). However, this example is not classified as a genuine ambiguity because the preference constraints single out one, most preferred interpretation. Following van der Sandt we speak of a genuine ambiguity when there is no single most preferred reading. Examples are cases where there are two possible antecedents for binding which are introduced at the same level. Example (11) would be an illustration of this, where nobody can tell which of the two men walking in the first sentence does the talking in the second. (11) A man was quietly walking down the street, when he was joined by another man. The man said: ... According to van der Sandt (1992:363) partial match examples also display a genuine ambiguity, and he claims that this is one of the phenomena that his theory can account for, while the satisfaction camp cannot. However, things appear to be somewhat more complicated.
3
T HE
PARTIAL MATCH PHENOMENON
The intuitive idea underlying the notion of a partial match can be explained in anaphoric terms. Consider a definite NP, along with a potential anaphoric antecedent. The plausibility of an anaphoric link between the two depends, among other things, on the ‘similarity’ between the two nouns. This is clear in extreme cases. For example, the woman cannot take a man as its antecedent. A full 6
or complete match corresponds with a high degree of similarity; a partial match corresponds with an intermediate degree of similarity; finally, one might speak of a complete non match when antecedent and anaphor are incompatible (as in the case a man; the woman).
3.1 The empirical facts Let us first take a closer look at what van der Sandt says about partial matches. Here are the examples put forward by van der Sandt (1992: 350-351). (12) a.
If John has an oriental girlfriend, his girlfriend won’t be happy. (= (1))
b. If John murdered his wife, he will be glad that she is dead. c.
If someone at the conference solved the problem, it was John who solved it.
According to van der Sandt, these sentences “display a genuine ambiguity” (van der Sandt 1992: 350); they have no single, preferred reading and this is due to the fact that the respective presuppositions “may but need not be bound to a potential antecedent” (van der Sandt, ibid.). All cases in (12) display a similar structure. In each case there is, as Soames (1982) put it, “a one-sided entailment between the antecedent and the presupposition of the consequent”. In other words, the antecedent is more ‘informative’ than the anaphor. Of course, this is only one of the possible relations between would-be antecedent and would-be anaphor. It is instructive to take a systematic look at the various pre-theoretic possibilities, which we loosely label as follows: I. antecedent is more ‘informative’ than anaphor, II. anaphor and antecedent are ‘incomparable’, III. anaphor and antecedent are equally ‘informative’, and IV. anaphor is more ‘informative’ than antecedent. Restricting ourselves to NPs: A is more ‘informative’ than B essentially means that the denotation of A is subsumed by the denotation of B . We make these notions formally precise in section 4.3. I. Antecedent is more ‘informative’ than anaphor The examples in (12) may be placed in this category. We have discussed one of them in somewhat more detail, namely (12.a). We fully share van der Sandt’s intuitions here, although the intuitions concerning example (12.a) might be a bit blurred due to a kind of lexical ambiguity in the word girlfriend (mistress/companion in life). However, it is not difficult to find examples that do not suffer from this problem. (13) If John buys a couple of Siamese cats, the pets won’t be happy. Here, the antecedent is more informative than the anaphor: the set of Siamese cats is a subset of the set of pets. Intuively, this sentence displays the same kind of ambiguity as (12.a). Thus (13) has a presuppositional reading (paraphrasable as there is a set of petsi , and if John buys a couple fo Siamese cats, then theyi will not be happy) and a non-presuppositional reading (if John buys a couple of Siamese catsi , theyi will not be happy). II. Anaphor and antecedent are ‘incomparable’ The following examples fall in this category: (14) a.
If John has sons, his young children will be spoiled.
b. If John talks to some partygoers, the children will laugh at him. Obviously, in both cases anaphor and antecedent are incomparable. Nevertheless, intuitively, these examples are ambiguous in the same way as the partial match examples discussed so far. Thus: example (14.a) is ambiguous between a non-presupposing reading (paraphrasable as if John has sons, the young ones among them will be spoiled) and a presupposing one (John has young childreni and if he has sons, theyi will be spoiled). Example (14.b) is ambiguous, in a similar fashion, between a 7
presupposing reading (there is some group of childreni and if John talks to some partygoers, theyi will laugh at him) and a non-presupposing reading (if John talks to some partygoers, the children among them will laugh at at him). Of course, example (14.b) can also have an identity reading (in which case all the partygoers are children). However, we contend that this is a special case of the last, non-presuppositional reading. Notice that for the identity reading, the definite the children is typically de-accented. In general, and simplifying somewhat, identity anaphors tend to be deaccented, while all other noun phrases must be accented (cf. Van Deemter 1994 for the fine print). Hence, accenting can sometimes have a disambiguating function. In particular, the lack of an accent on ‘children’ in (14.b) signifies that all the partygoers are children, whereas an accent on ‘children’ signifies that the children are either a real subset of the set of partygoers or some other set of children — but not the entire set of partygoers that John talks to. III. Anaphor and antecedent are equally ‘informative’ Consider the following examples: (15) a.
If Fido catches a cat, the cat must be old.
b. If Fido catches a cat and a mouse, he will chase the cat and devour the mouse. The first example is a clear case of a full match (the set of cats is equal to the set of cats). Intuitively, sentences like (15.a) do not display an ambiguity. Such examples, containing full descriptions, are slightly marked; a pronoun would sound more natural. However, it is easy to construct natural examples involving fully matching descriptions along the lines of (15.b). IV. Anaphor is more ‘informative’ than antecedent Notice that when an anaphor is more informative than its antecedent, it triggers a presupposition which presents new information. However, the distribution of such examples is somewhat limited. For instance, it is difficult to find conditional examples which fall in category IV. Consider: (16) a.
If John has a girlfriend, his oriental girlfriend won’t be happy.
b. If John owns a donkey, he will be worried about the purple farmer-eating donkey on the loose. (after Beaver 1995:61) For both these examples, the presupposing reading seems strongly preferred over the non-presupposing one, which is at best marginal. In other words, these sentences do not seem to be ambiguous. In Krahmer (1995:165) it is hypothesized that identity anaphora can only add information if the antecedent is interpreted specifically. Let us formulate this as the Informative Anaphors Hypothesis.2 I NFORMATIVE A NAPHORS H YPOTHESIS (IAH) A potential antecedent with a non-specific interpretation, which is less informative than the anaphor under consideration, does not qualify as a suitable antecedent for the anaphor, provided that the relation between anaphor and potential antecedent is one of identity. 2
There do exist some potential counter-examples to the generalization proposed in the IAH. Consider, for example the following ‘politically correct’ usage of the female pronoun. (17)
If the reader has studied example (17), she might come to the conclusion that it constitutes a counterexample to the IAH.
However, we are unsure whether examples such as (17) are real counterexamples to the IAH. For instance, it has been argued by various people that pronouns are essentially devoid of semantic content (by van der Sandt 1992 to give but one example), so to what extent can they add information?
8
Thus: an (indentity) anaphor can only add information about its antecedent when the antecedent has a specific interpretation, and this would account for the fact that the examples in (16) defy categorization as partial matches. The IAH only applies when the relation between anaphor and potential antecedent is one of identity, that is: when antecedent and anaphor refer to the same (set of) object(s). This qualification is made, because it seems possible for anaphors to add information about a subset of their antecedent. Consider: (18) If Barney owns cows, then he will feel sorry for the mad cows. Clearly, mad cows (where mad carries as accent) is more ‘informative’ than cows. And contrary to examples such as (16), this example displays an intuitive, genuine ambiguity between a nonpresupposing reading (paraphrasable as if Barney owns cows, then he will feel sorry for the mad cows he owns) and a presupposing one (there are mad cowsi , and if Barney owns cows, then he will feel sorry for themi ). Thus, examples of type IV also display a partial match ambiguity, as do types I and II, but factors such as the IAH complicate the picture somewhat. Summarizing. We distinguished four kinds of relations between would-be anaphor and would-be antecedent. When an anaphor is not equally ‘informative’ as its would-be antecedent (i.e., the two have a different denotation) we have a partial match. Such sentences display a genuine ambiguity between a presupposing and a non-presupposing interpretation, but sometimes other factors may cause disambiguation. In particular, we have seen that continuations, de-accenting and the Informative Anaphors Hypothesis (the IAH) may eliminate one of the interpretations. Let us now look at the predictions the theory of Van der Sandt (1992) makes regarding the examples discussed above. As we shall see, if we apply the formal theory of van der Sandt (1992) to the three kinds of partial matches, we encounter a number of problems.
3.2 Van der Sandt’s predictions I. Antecedent is more ‘informative’ than anaphor Let us reconsider van der Sandt’s own (12.a), and let us construct a DRS for this example. As before, we assume that his has already been resolved as John’s. (DRS 6)
x x = john y oriental(y) girlfriend(y) poss(x; y) =)
:
happy(z) z @ girlfriend(z) poss(x; z)
If we feed (DRS 6) to van der Sandt’s resolution algorithm, it will first start looking for an accessible and suitable antecedent for the presuppositional DRS: it seeks a discourse referent which is accessible and which satisfies the conditions of being a girlfriend, and standing in the possessive relation with John. But such a referent is easily found: y meets all the conditions. So it is unclear how van der Sandt (1992)’s algorithm can avoid binding the presupposition, which would make 9
the non-presupposing reading (given in (2.a)) the primary reading of (12.a) (by definition 1) and hence would predict that this example is not a genuine ambiguity after all. We do not consider this to be a point of great importance by itself, but it does indicate that van der Sandt’s formal theory does not fully implement the intuitions sketched in the first part of van der Sandt (1992). II. Anaphor and antecedent are ‘incomparable’ The same problem applies as in category I. and other, more serious, problems apply in addition. Consider, for example, (14.a), repeated below for convenience. (19) If John has sons, his young children will be spoiled. (DRS 7) is the van der Sandtian representation for this example. Again: assume that his has been resolved as John’s. We follow the notation for plurals used by van der Sandt (1992:370). The capitals are discourse referents standing for sets of objects. It should be noted that all predicates in this article are ‘strictly distributive’ in the sense of Kamp & Reyle (1993, 407). E.g., young child(X ) has the intuitive interpretation that all elements of X are young children. In Kamp & Reyle (1993) this is denoted as young child (X ). We omit the superscript where this can be done without creating confusion. (DRS 7)
x x = john Y son(Y ) poss(x; Y )
=)
spoiled(Z ) Z @ young child(Z ) poss(x; Z )
If we feed (DRS 7) to the algorithm, it will look for an accessible, suitable antecedent for the presupposition triggered by his young children. It is not entirely clear to us whether sons is a suitable antecedent for his young children according to van der Sandt’s algorithm (presumably it is), but it yields undesired results either way. Suppose the algorithm decides that Y (the sons) is not a suitable antecedent for Z (the presupposed young children). In that case, the van der Sandtian preference order given in definition 1 tells us that the presupposing reading, achieved by accommodating the presupposition, is the single most preferred reading for (14.a). In other words, (14.a) does not display a ‘genuine ambiguity’ as partial match examples should do. If, by contrast, Y (the sons) is a suitable antecedent for Z (the young children), binding is preferred and, as before, no ambiguity results. In the latter case, there is an additional problem, which has nothing to do with preferences between interpretations. If the presupposition gets bound, it is ‘absorbed by the antecedent’, and this results in a reading which may be paraphrased as follows:3 3
To avoid a possible confusion: we are aware of the fact that paraphrasing DRSs in natural language is not always an easy matter. Both Geurts (p.c.) and van der Sandt (p.c.) objected to this paraphrase by saying that it blurs the distinction between asserted material (sons) and presupposed material (young children). This is true, and we fully agree that this distinction is important (see e.g., Krahmer 1996, 1998). However, (i) the theory presented in van der Sandt (1992) makes no distinction between asserted and presupposed material in the resolved DRS. And (ii) the main point of our paraphrase is to indicate that the presuppositional material ends up in the antecedent of the conditional.
10
(20) If John has young sons, they will be spoiled. This reading seems wrong. First of all, in our opinion binding can also appear in situ, that is: the presupposition to be bound should not necessarily be merged with the target DRS, but may also be merged with the source DRS. Consider yet another example: (21) If John has children, he’ll spoil the little bastards. We are well-aware of the fact that epithets like little bastards have some pecular properties (see below). Nevertheless, they serve nicely to further illustrate the point about in situ binding. If we bind the presupposition triggered by the definite description in van der Sandt’s way, we end up with a reading which may be paraphrased as if John has children and they are little bastards, then he’ll spoil them. That is: the children are only spoiled if they are little bastards. In our opinion, the right reading is something like if John has children, they’ll be little bastards and he’ll spoil them. Moreover, we feel that, for the non-presuppositional reading of (14.a), there is no reason to assume that the young children should be identified with the sons (as is done in (20)). The only thing we can safely say is that the young children are a subset of the sons. In sum, we think that (14.a) has a binding reading paraphrasable as (22). (22) If John has sonsi , the young ones among themi will be spoiled. As said, we view the situation in which all the sons happen to be young as a special case of this interpretation, typically marked by a complete absence of accents in the NP his young children (cf. van Deemter 1991, 1992). It is worth pointing out that the two problems we mentioned in connection with the paraphrase (20) are independent of each other. In fact, some people informed us that, besides (22), they could also conceive of an interpretation of (14.a) in which the anaphor is bound subsectionally but not in situ: (23) If John has sonsi and somej of themi are young, then thesej will be spoiled. We agree that (23) is a possible reading of sentence (14.a). Below we return to this issue. III. Anaphor and antecedent are equally ‘informative’ Above we argued that the examples in this category (the ‘full’ matches) intuitively do not display a genuine ambiguity. The theory of van der Sandt (1992) correctly predicts that the binding interpretation of the examples in (15) is the most preferred one. It is interesting to note that the accommodation reading, while less preferred, is not ruled out. Reconsider example (15.b), and suppose that the presuppositions triggered by the cat and the mouse have been globally accommodated. The resulting reading is not ruled out by the informativity constraint, since this constraint is defined in terms of redundant (sub-)DRSs, and the antecedent-DRS contains non-redundant information, namely that Fido chases a cat and a mouse. Nevertheless, it seems that the accommodation reading for sentences like (15.b) is simply not available. Therefore, Krahmer & van Deemter (1997) have argued that some sort of informativity constraint should also apply at the level of NPs. However, a full discussion of this issue falls outside the scope of the current article. IV. Anaphor is more ‘informative’ than antecedent As for the fourth group of examples, the reader may easily verify that the same problems are encountered here as in case II: van der Sandt’s algorithm fails to predict the genuine ambiguity of the sentences in this category and binding is defined in a way that may yield incorrect interpretations.
11
4
M ODIFYING
THE PRESUPPOSITIONS- AS - ANAPHORS APPROACH
In section 3.1 we argued that an anaphor and an antecedent stand in a partial match relation if the two are not equally informative, i.e., not co-extensive. Moreover, in the case of a partial match, a sentence is genuinely ambiguous between a presupposing and a non-presupposing reading. In other words, we support the intuition sketched in van der Sandt (1992:349-351). However, if we apply the formal theory (i.e., the presupposition resolution algorithm) of van der Sandt (1992) to the partial match examples (as done in section 3.2), we encounter essentially two problems: (i) the algorithm does not generate the required genuine ambiguity in the case of a partial match, and (ii) not all the binding readings are correct. To remedy these problems, we propose a modified version of van der Sandt’s resolution mechanism. One central ingredient is the use of so-called context variables. Binding is viewed as contextually restricted quantification, where the relevant context is provided by the anaphoric antecedent. Accommodation is taken to be a contextually restricted variant of the usual accommodation procedure. To arrive at all the different possible (binding or accommodation) interpretations of a given sentence containing a presupposition, we exploit van der Sandt’s resolution mechanism, with its use of unresolved representations. However, we make some modifications to the resolution mechanism as such, taking the notion of partial match into account by paying more attention to properties of potential antecedents. When antecedent and anaphor stand in a partial match relation, the algorithm generates a genuine ambiguity. This entails that our modification of the algorithm yields a modified, partial preference order between possible interpretations. One of the attractive features of van der Sandt (1992) is that it aims at developing a uniform mechanism treating all presupposition triggers in exactly the same way, namely as anaphors looking for an antecedent. A disadvantage of this bird’s eye view on presuppositions is that a number of details (such as the issues we are concerned with here) are not sufficiently spelled out. We take it that this is one of the factors which has lead to a certain confusion of tongues on the partial match phenomenon in the first place. Therefore we first opt for a frog’s perspective on presupposition projection at first, focussing on one kind of presupposition triggers: definite descriptions. Later, we slightly broaden our horizon by taking all noun phrases into consideration. To start, however, we have to do some formal groundwork.
4.1 Preliminaries Van der Sandt (1992) is mostly based on the DRT fragment as it was defined in Kamp (1981). The kind of examples we are interested in, and the treatment we have in mind for them, calls for two extensions of this basic DRT fragment. Plurality and quantification in DRT The issue of plural quantification is known to be complex, and combining it with the dynamic interpretation underlying DRT only adds to the number of complications. In the following, we adopt the basic treatment of plurality and quantification outlined in Kamp & Reyle (1993, ch. 4). Kamp & Reyle use an algebraic ‘Link-style’ (Link 1983) interpretation of plurality, in which the domains contain atomic as well as non-atomic entities. Following the convention of Kamp & Reyle (1993), we use boldface lowercaps variables (x, y, z, ...) to range over both individual (or atomic) referents and plural (non-atomic) referents. Lowercase variables (x; y; z; ...) are used for individual referents, and uppercase variables (X; Y; Z; ...) for plural referents. This convention entails that general definitions contain boldface referents, and actual examples do not. We also adopt the treatment of generalized quanitifiers in Kamp & Reyle (1993, ch. 4) in terms of duplex conditions. In general, a generalized quantifier (which we shall denote as DET) is a relation between two sets of (atomic) entities, say A and B , and is represented by Kamp & Reyle as a 12
condition of the following form, where A0 is a DRS representing A, and B 0 a DRS representing B .
A
0
?@ ?DET @ ? @@ x @ ? ? @?
B
0
The leftmost DRS of this duplex-condition is called the restrictor and the rightmost DRS the scope, the capsized box in the middle is the quantifier. The DET gets its usual interpretation as given in generalized quantifier theory (GQT, see e.g., Barwise & Cooper 1981; for technical details on generalized quantifiers in DRT we refer to Kamp & Reyle 1993:425-427). For example, here are the standard GQT-style definitions of singular and plural the (with d and d0 atomic):4
the (A)(B ) is true with respect to a model M iff 9d 2 D (d 2 A & 8d0 2 D (d0 2 A ) d0 = d) & d 2 B ) the (A)(B ) is true with respect to a model M iff 9d 2 D (d 2 A & 8d0 2 D (d0 2 A ) d0 2 B )) sg
pl
It is worth pointing out that Kamp & Reyle still distinguish indefinites from truly quantificational determiners (like five, all), and we follow this practice. Concretely, this means that indefinite NPs of the form DET CN, where DET is either a(n), some or empty (in the case of bare plurals) introduce a fresh discourse referent in the current DRS. Context variables In Westerst˚ahl (1985) the notion of contextually restricted quantification is introduced, motivated by examples such as the following: (24) The children were having a lot of fun. Clearly this is not a statement about all the children in the universe. According to Westersta˚hl, the definite determiner acts as a “context indicator which signals the presence of a context set C” (Westerst˚ahl 1985:60) in such a way that the children denotes C \ child, i.e., a contextually restricted subset of the set of all children. Westerst˚ahl himself immediately noted that there is a strong connection between discourse referents and context variables (Westerst˚ahl 1985:70). In our revision of the presuppositions-as-anaphors theory, we use context variables, which we represent as C; C 0 ; : : : These context sets are just discourse referents. Below, we let every NP introduce a fresh ordinary discourse referent as well as a fresh context set, and our modified presupposition resolution algorithm explicitly operates on the latter. Here, a context set C is either equated with a previously introduced discourse referent, or with the entire domain of discourse. We have made this simplifying assumption in order to stick as closely as possible to van der Sandt (1992). In any case, the output of our presupposition resolution algorithm is a DRS from which the context set C can be eliminated. Thus, the use of context sets merely facilitates the resolution process. Besides introducing contextual variables, we also employ ‘contextually restricted’ predicates. That is, we use conditions like manC (john) which have as intuitive interpretation: John is a man and an element of the context set C . Formally, if is a noun representation:5
h
4
i
Here and elsewhere we assume that a model M is a tuple of the form DM ; IM , where DM is the ‘domain of discourse’. DM consists of a set of atomic entities D and an associated partial ordering , together forming an atomic, free, complete upper semi-lattice with zero, cf. Kamp & Reyle (1993:425). IM is an interpretation function (combining NameM and PredM , Kamp & Reyle passim). We drop the M subscripts on domain and interpretation function where this can be done without creating confusion. 5 These clauses are variants of cause (ii:g:i) of definition 4.3.7 of Kamp & Reyle (1993:426). Recall our remark that all predicates used in this article applied to plural (non-atomic) discourse referents are strictly distributive. That is: IM ( ) = X y X : y IM ( )
f j8 2
2
g
13
M j= (x) iff f (x) 2 I () \ f (C ) M j= (X ) iff f (X ) 2 I ( ) \ f (C ) f
f
C
M
C
M
4.2 Definite descriptions and the presuppositions they trigger Definite descriptions, phrases of the form [the CN] (where CN is a possibly complex common noun phrase), are generally assumed to trigger an existence presupposition, that is: the CN denotation is presupposed to be non-empty. We model this as follows: a definite description presupposes that there is some context set C which has a non-empty intersection with the CN denotation. When the DRS construction algorithm encounters a definite description, the following rule (temporary version) is activated.6
[DET CN] Rule, for DET = the
Upon encountering an S of the form or a VP of the form , with a definite description (of the form the CN[ sg]), replace S or VP with the following presuppositional DRS and duplex condition, where y and z are fresh discourse referents and C is a fresh context variable.
?@@ ? ?they @ @@ ?? @?
y
sg
CN (y ) C
@
y
C; z C
CN (z)
Here CN is the representation of CN (in singular form), and z is z or Z depending on the number of the CN.7 To illustrate this rule, consider example (14.a) again, here repeated as (25). (25) If John has sons, his young children will be spoiled. This sentence is represented by ( DRS 8). The bare plural sons is indefinite: it introduces a fresh (non-atomic) discourse referent Y . The possessive NP his young children is handled by our definite descriptions rule (by analyzing the possessive as the young children of him): it introduces a presuppositional DRS, with the intuitive interpretation that there is some context set C which contains John’s young children, and a duplex condition, which expresses that all of John’s young children in this context set C will be spoiled.
6
This rule is an instance of CR.NP [Quant = +], Kamp & Reyle (1993: 318, 347). Below it is replaced by a more general rule. The referent z is an atomic referent when the CN is [+ sg] and a non-atomic referent when the CN is [ sg]. In other words: we assume that the child presupposes the existence of at least one child and that the children presuppose the existence of at least two children. Nothing hinges on this assumption. Suppose for instance that one wants the existence presupposition always to be ‘at least one’, in that case z should always be an atomic referent. 7 Remember that CN (Z ) and CNC (Z ) should be read as CN (Z ) and CNC (Z ) respectively.
?
14
(DRS 8)
x x = john Y son(Y ) poss(x; Y )
=)
v young child (v ) poss (x; v ) C
C
?@ ? ? the @@ @@ v ? @?? pl
spoiled(v )
C; Z @ young child (Z ) poss (x; Z ) C
C
The resulting DRS can only be interpreted after the presuppositional DRS contained in it has been resolved.
4.3 The modified presupposition resolution algorithm When van der Sandt’s resolution algorithm encounters a presuppositional DRS it will first try to bind this presupposition to an antecedent, and our modified algorithm will do the same. This immediately raises a question: what qualifies as an antecedent? The answer of van der Sandt (1992) is simple: every suitable discourse referent which is accessible from the DRS containing the presuppositional DRS is a potential antecedent. Van der Sandt does not specify what makes a referent suitable. In our opinion, the main factor in determining the suitability of a discourse referent is the phrase which lead to the introduction of the referent in the first place. It is difficult to find examples which illustrate this, and where factors like discourse structure, focus-ground partitions etc. are neutralized, but here is an attempt. (26) a.
Yesterday, an1 uncle of mine bumped into a2 man. Thei man fell to the ground.
b. Yesterday, a2 man bumped into an1 uncle of mine. Thei man fell to the ground. We contend that in both (26.a) and (26.b), the definite the man is strongly preferred to be coindexed with a man (i.e., i = 2), even though obviously both 1 and 2 are male persons. This is due to the fact that 1 is introduced as a man, while 2 is introduced as an uncle. This shows that the resolution algorithm should not only take the accessibility of discourse referents into account, but also properties of the phrase which lead to the introduction of the referent.8 Here we are particularly interested in the possible values which a discourse referent can have according to the denotation of the phrase with which the referent is associated. For this purpose, we use value sets. For the examples in (26) it is the CN which determines the relevant value set. But for other phrases which lead to the introduction of a referent (e.g., proper names) this may be different. 8 This entails that an interpreter has to remember how an object was introduced. Jarvella & Herman (1972) have shown that listeners are good in recalling the last sentence they heard, but that recall of less recent material soon declines to ‘nearly chance level’. Interestingly, Bates, Masling and Kintsch (1978) have shown that when the function of an utterance is to introduce new referents literal memory improves.
15
In general: suppose that a phrase leads to the introduction of an (atomic of non-atomic) discourse referent x and a DRS . Then the value set of x in a model M and with respect to an assignment f (assigning values to the free discourse referents in ), is defined as follows: VAL
(x; [ ]] ) =def fd 2 D j M j= [hx i g M;f
f
;d
For example, consider the indefinite description a man with a hat, and suppose that it triggers the introduction of a discourse referent y . Then the value set of y is given by: VAL (y; [ [y; z j man(y ); hat(z ); with(y; z )] ] M;f ) = fd 2 D j d 2 I (man) & 9d0 2 D (d0 2 I (hat) & hd; d0 i 2 I (with))g
In words: the value set of y in M is the set of men with a hat in M . Throughout this article we suppress the M and f subscripts whenever this can be done without creating confusion. Notice that in the case of atomic predicates P, the value set VAL(x; [ P(x)]]) equals the predicate denotation [ P] . In those cases, we use the predicate denotation as value set. Below we take antecedents to be pairs hx; VAL(x; [ ]])i consisting of an accessible discourse referent and a corresponding value set. Before we sketch our modified resolution algorithm, let us say something about the influence of the hearer’s background knowledge. Consider the following example of a partial match. (27) If John has sons and a TV set, his children will watch a lot of football. In general, the denotations of the anaphor (his children) and the antecedent (sons) are not equal. However, if an interpreter thinks that it is common knowledge that, due to some genetic peculiarity, John and his better half can never have daughters, this example only has a non-presupposing reading for the interpreter. Therefore, our algorithm does not quantify over all possible models, but rather over all models which are in accordance with the interpreter’s view on the common ground. For the current example, this would mean that the interpreter’s H-models (H for hearer) will not include models in which John has daughters. In what follows, specific hearer knowledge will not be taken into account, unless noted otherwise. Now we are in the position to present the modified resolution algorithm. We formulate the algorithm in a slightly more general manner than required for the treatment of definite descriptions. This will be beneficial later on, when we extend the treatment of definite descriptions to cover essentially all kinds of NPs. The input of the algorithm is an underspecified DRS containing at least one unresolved presuppositional DRS. As we have seen, for definite descriptions this presuppositional DRS is of the form: (DRS 9)
@
C; y
CNC (y)
In the case of embedded presuppositional DRSs (i.e., one presuppositional DRS subordinates a second presuppositional DRS) the algorithm should first be applied to the most deeply embedded one, as is the case with van der Sandt’s original algorithm. For each presuppositional DRS there is a list of potential antecedents, and as argued above this is a list of accessible referents and their respective value sets. This list is ordered by nearness to the presuppositional DRS, i.e., the first element on the list is the nearest referent and the last element is the one farthest away. Simplifying slightly, this list can be written as follows:9 9
A more accurate modeling would make PA a partial order (because several discourse referents may be introduced at the same level and these are ‘equally far away’ from the source-DRS), but we ignore this here for the sake of simplicity. Nearness is formally defined in terms of subordination. Thus: a is nearer to a DRS than b iff (i) a and b are introduced in different DRSs, (ii) the DRS in which b is introduced subordinates the DRS in which a is introduced, and (iii) the latter DRS subordinates . a and b are equally near to if neither a nor b is nearer to than the other.
16
LIST OF POTENTIAL ANTECEDENTS :
PA = hhx1 ; VAL(x1 ; [ 1 ] )i; : : : ; hxi ; VAL(xi ; [ i ] )i; : : : ; hxn ; VAL(xn ; [ n ] )ii The modified resolution algorithm is now going to try and bind the presuppositional (DRS 9), triggered by the definite description, to an element of the list of potential antecedents, by comparing the value set of the presupposition with the value sets of the potential antecedents. Let PRESM;f be the value set in M with respect to f of the referent associated with the phrase which triggers the presupposition (again suppressing subscripts where possible). Thus, for definite descriptions, which trigger presuppositions of the form ( DRS 9), we have the following value set: PRESM
= VAL(y; [ [C; y j CN (y)] ] ) = VAL(y; [ [y j CN(y)] ] ). C
M
M
Similarly, let ANTiM;f be the value set of the i-th accessible discourse referent in M with respect to f (thus, ANTiM;f abbreviates VAL(xi ; [ i ] M;f ), for some hxi ; VAL(xi ; [ i ] M;f )i 2 PA ). Then the resolution algorithm can be described as follows: IF 9i(PRESM
= ANT
i M
, in all H-models M )
THEN BIND
ELSE IF 8i(PRESM \ ANTiM THEN
= ;, in all H-models M )
ACCOMMODATE
ELSE (Partial Match!) BIND
OR ACCOMMODATE
In words: the algorithm first checks if there is a potential antecedent with the same denotation as the presupposition in all H-models. If it finds one, it is a full match and the presupposition will be bound (both the BIND and the ACCOMMODATE operation are defined below). As in van der Sandt (1992): if there is more than one fully matching antecedent, then the presupposition will be bound to the nearest one; if there are two or more equally near fully matching antecedents, an unresolvable ambiguity results (cf. example (11)). If the value set of the presupposition is disjoint with the value sets of all potential antecedents, the presupposition is accommodated. The other cases are partial matches: there is no antecedent with the same value set as the presupposition, but there is an antecedent which matches partially, i.e., has a non-empty intersection with the presupposition in some H-model. In those cases the presupposition can either be accommodated or bound to this partially matching antecedent. Before we can return to our example, we have to define the notions BIND and ACCOMMODATE. To begin with the former, it follows from the algorithm that we BIND the presuppositional (DRS 9) if an antecedent hxi ; ANTiM i 2 PA has been found such that ANTiM is either coextensive with the value set PRESM in all H-models M (full match), or has a non-empty intersection with it in some H-model M (partial match). D EFINITION 2 (BIND) hxi ; ANTi i is the nearest antecedent in PA : 1. merge the presuppositional DRS with the source DRS, and 2. add a condition C
=x
i
to the source DRS
17
This definition of binding differs in two significant ways from the usual definition due to van der Sandt (1992). First and foremost, it generalizes to non-identity anaphors since only the context set is equated with a set of objects. And second, the presuppositional DRS is not moved to the target DRS (where xi was introduced). Thus, this definition leaves the bound presupposition in situ. We illustrate this below for example (25). ACCOMMODATE is defined as follows: D EFINITION 3 (ACCOMMODATE) The main DRS is the (initial) target DRS: 1. remove the presuppositional DRS from the source DRS and merge it with the target DRS, 2. add a condition C
= D to the target DRS10
3. check whether the result satisfies the conditions (consistency, informativity etc). If not, redo 1-3 with a new target DRS: the one (on the projection line) immediately subordinated by the old target DRS. The second clause states that the context variable C is equal to the domain of discourse, thereby neutralizing the effect of C . It is worth emphasizing that this is done to keep the differences with van der Sandt to a minimum: it entails that our ACCOMMODATE amounts to the same operation as van der Sandt (1992)’s accommodation. As in van der Sandt (1992), the target DRS is preferably the main DRS, but if this results in a unacceptable DRS (inconsistent, uninformative, ...), accommodation may occur in target DRSs closer to the source DRS. The modified algorithm implies the following partial preference order between interpretations, which splits clause 1 from Definition 1 up into clauses 1 and 2 in Definition 4. D EFINITION 4 (Modified partial preferences) 1. Binding to a fully matching antecedent is preferred over accommodation. 2. Binding to a fully matching antecedent is preferred over binding to a non-fully matching antecedent. 3. Accommodation is preferred to occur as ‘high’ (far away from the source DRS) as possible. 4. Binding is preferred to occur as ‘low’ (near the source-DRS) as possible. Let us go back to our example (25) and its associated (DRS 8), both repeated below for the sake of convenience. (28) If John has sons, his young children will be spoiled.
10
The constant D refers to the domain of discourse: [ D] M
18
= IM (D) = DM .
(DRS 10)
x x = john Y son(Y ) poss(x; Y )
=)
v young child (v ) poss (x; v ) C
C
??@@@ ?@ the ? @ v? @? pl
spoiled(v )
C; Z @ young child (Z ) poss (x; Z ) C
C
(DRS 10) is the input for our modified resolution algorithm. The list of potential antecedents for the presuppositional DRS is: hhY; [ son] i; hx; fjohn gii. Let us assume that there is no specific hearer knowledge. Then there will be an H-model M such that PRESM (the set of John’s young children) =6 [ son] M . In other words: there is no full match between sons and his young children. However, 6 ; (after all, it may well be that there will also be an H-model M in which [ son] M \ PRESM = some of the sons are young children). In other words: the algorithm predicts that this is a partial match, and a genuine ambiguity between a binding and an accommodation reading ensues. (DRS 11) results when we BIND the presuppositional DRS. (DRS 11)
x x = john Y son(Y ) poss(x; Y )
C; Z young child (Z ) poss (x; Z ) C=Y v C
=)
C
young child (v ) poss (v; x)) C
C
?@@ ? ? @ @@thev ?? @? pl
spoiled(v )
This DRS can be paraphrased as If John has sons, then there are young children among them and these will be spoiled, or more concisely as (29). (29) If John has sons, then the young ones will be spoiled. The second reading comes about via a global application of ACCOMMODATE. The result is (DRS 12). 19
(DRS 12)
x; C; Z x = john young child (Z ) poss (x; Z ) C=D Y son(Y ) poss(x; Y ) C
C
=)
?@@ ? ? @ @@thev ?? @?
v child (v ) poss (x; v ) C
pl
C
spoiled(v )
This interpretation can be glossed as follows: (30) John has youngi children, and if he has sons, theyi will be spoiled. Summarizing, if we feed the representation of example (25), (DRS 10), to the modified resolution algorithm, it decides that there is a partial match between the presupposition triggered by the description his young children and its antecedent sons. The corresponding ambiguity is between ( DRS 11) and (DRS 12) for the non-presupposing/binding and presupposing/accommodation interpretation respectively. So far, we have discussed a refined and modified version of van der Sandt’s presupposition resolution mechanism, and applied it to presuppositions triggered by definite descriptions. We have assumed that definite descriptions trigger an existence presupposition, more precisely: the CN presupposes that the intersection of the CN denotation with a given context set is not empty. Compared with the resolution algorithm of van der Sandt (1992), our version is different in three respects: (i) it is more explicit in what counts as a potential antecedent (namely a pair consisting of a discourse referent and its value set), (ii) it is more explicit about the relation between presupposition and potential antecedent, explicitly distinguishing full match, no match and partial match, and generating the required ambiguity in the latter case, and (iii) binding is a different operation, defined using contextual quantification: it generalizes to non-identity cases and the presuppositional DRS remains in the DRS where it originated. Two well-known ‘difficult’ phenomena often associated with definite descriptions are bridging and epithets. How do these fit in with our proposals? Consider the following bridging example: (31) If John buys a car, he checks the motor first. The definite description the motor presupposes the existence of a motor. Clearly, the presupposition triggered by the motor does not even match partially with one of the potential antecedents (John and a car). Hence, (global) accommodation of the presupposition is predicted. The fact that cars have motors is not taken into account at all. In Krahmer & Piwek (1997) and Piwek & Krahmer (1997) it is shown how van der Sandt’s presuppositions-as-anaphors theory can be combined with a constructive inference system, which allows for a formal interaction between presupposition resolution and world knowledge. What is relevant for our purpose here, is that a piece of world knowledge stating that cars have motors can be used to bind the presupposition to an implied antecedent (the motor of the car mentioned in the antecedent). In this case, the presupposition triggered by the motor fully matches the implied antecedent, but as one would expect, presuppositions can 20
also match partially with implied antecedents. The more ‘difficult’ cases of bridging (such as (32), from Haviland & Clark 1974:514-515) illustrate this. (32) Mary got some picnic supplies out of the car. The beer was warm. Even though the approach to world knowledge advocated by Krahmer/Piwek is explicitly subjective, it is unlikely that the interpreter has a piece of world knowledge to her disposal to the effect that picnic supplies include beer. In general, world knowledge will allow the interpreter to infer food and beverage. Hence the presupposed beer will only match partially with the implied beverage. Epithets are definite descriptions like the poor woman, the little bastards, etc. They differ from ordinary descriptions in that they are not interpreted literally (the poor woman may be a millionaire and the little bastards can be legitimate children) and have a very strong preference for being bound. In particular, they do not appear to give rise to partial match ambiguities. Consider: (33) If John has an oriental girlfriend, then we feel sorry for the poor woman. Example (33) does not display a partial match ambiguity; it only has a non-presupposing/binding reading. We claim that this is due to the fact that epithets essentially behave like pronouns, and as noted in the introduction, pronouns cannot be accommodated (we discuss this property below in more detail). One could say that epithets are pronouns that are emotionally dressed up by the speaker, i.e., express something of the speaker’s attitude towards the designated referent. To back up this claim, consider the following example, which is Geurts’ (1995:47) variant of Karttunen’s (1969) paycheck sentence. (34) The man who fed his German shepherd on tandoori chicken was beaten by the man who restricted fits/the poor animal’s/his dog’sg diet to broccoli. Focussing on the sloppy identity reading, Geurts notes that the pronoun it and the epithet the poor animal can be read as his German shepherd, but that such a reading is not available for the phrase his dog; in that case the breed of dog owned by the second man is left open. This, admittedly circumstantial, evidence indicates that epithets should be analyzed as pronouns rather than as full definite descriptions. Consequently, we assume that they will always be bound.
4.4 Extending the presuppositions-as-anaphors approach In the previous section we have outlined a modified version of the presuppositions-as-anaphors algorithm and applied it to definite descriptions. There seem to be few impediments to extending the resulting theory in several ways. For one thing, we would like to believe that the treatment of definite descriptions carries over to definite NPs in general. It is common practice to analyse possessives as definite descriptions, thus John’s oriental girlfriend is seen as shorthand for the oriental girlfriend of John. Moreover, various people have argued that proper names too can be seen as definite descriptions of the form the individual named such and such.11 Thus, the proper name John can be understood as the individual named ‘John’. It has been observed (e.g., by van der Sandt 1992:375) that such a presuppositional analysis of proper names improves upon the standard DRT treatment, in which proper names are always inserted in the main DRS, in that it allows proper names to be ‘bound’ occasionally. Consider the following example, which does not appear to have a presupposing reading. (35) If parents decide to name their child ‘Barf’, we know in advance that Barf will have a hard time in school. 11
See e.g., Russell (1919:174) and Kneale (1962). This proposal was criticized by Kripke (1980: 68-73). Cresswell (1985) and Bach (1987) have proposed refutation of Kripke’s criticism. See Geurts (1995:23) for some discussion.
21
Notice that even though proper names can be bound, they do not seem to give rise to partial match ambiguities. Take example (36). (36) If a man enters the room, Bill whistles. Intuitively, example (36) only has a presupposing reading. The presupposition triggered by Bill cannot be bound to a man, even though the value sets for Bill and man presumably stand in a partial match relation (since Bill is typically a masculine name). We contend that this is due to our Informative Anaphors Hypothesis, which stated that an antecedent which is less informative than the anaphor does not qualify as a suitable antecedent. Finally, we adopt the fairly common treatment of pronouns as lightweight descriptions. Thus, a pronoun like he is analysed as the male individual (cf. e.g., Geurts 1995:23). Interestingly, just like proper names, pronouns do not seem to give rise to partial match ambiguities. Consider: (37) If a doctor enters the room, he whistles. Here the situation is precisely the inverse of the proper name situation. Even though according to our criteria, the value sets associated with doctor and he (or: male individual) stand in a partial match relation (both men and women can be doctors), the presupposition associated with the pronoun cannot be accommodated. This follows from van der Sandt’s claim that pronouns and ‘other kinds of semantically less loaded anaphors’ cannot be accommodated, since they do not carry sufficient descriptive content (van der Sandt 1992:344-345). Van der Sandt founds his claim on pairs such as (38). (38) a.
Jack’s dog is bald.
b. It is bald. According to van der Sandt the presupposition that Jack has a dog is accommodated in (38.a) and hence this sentence receives a normal interpretation. Example (38.b), however, does not get an interpretation because the pronoun does not have an antecedent. We agree with van der Sandt’s claim, and take it that this explains why the partial match in (37) is disambiguated in favor of the non-presupposing/binding reading. We believe that this claim should be placed in a wider perspective. For example, it seems to us that both (39.a) and (39.b) are not interpretable without context, even though only the latter contains a pronoun. (39) a.
The man is bald.
b. He is bald. In our opinion, this illustrates that van der Sandt’s claim should be related to semantic content, rather than form. This might also explain why for certain sentences in which there is a partial match between anaphor and antecedent only a binding interpretation seems available. For instance, Dekker (p.c.) pointed out that there is an intuitive difference between (27), repeated here as (40.a), and (40.b). (40) a.
If John has sons and a TV set, his children will watch a lot of football.
b. If John has sons and a TV set, the children will watch a lot of football. Even though both sentences are partial match cases and our modified resolution algorithm predicts both are genuine ambiguities, it seems that for example (40.b) the anaphoric, non-presuppositional reading is preferred.
22
Summarizing: the observations made above indicate that the specific behavior of pronouns and proper names seem to provide no obstacles for a generalization of the analysis of definite descriptions from the previous subsection to definite NPs in general. Let us now investigate the possibility of generalizing the treatment of definite description to all NPs. As was explained in section 4.2, our proposed treatment of definite NPs rests on the use of contextual restrictions on both the assertional and the presuppositional part of what is expressed by a definite NP. The first restriction results in contextually restricted duplex conditions; the second restriction results in a presuppositional DRS of the form [C; y j CNC (y)]. Moving from definite to non-definite NPs, it seems plausible enough that our treatment of the assertion (i.e., the contextually restricted duplex conditions) may be re-used. However, in this section we would like to argue that the parallels between definite and non-definite NPs go even further than this, extending into the presuppositional part of what the NP expresses. We would like to make a rather strong claim: that a non-definite NP can express exactly the same (existential) presupposition as a definite NP. This assumption is exploited to arrive at an analysis of non-definite NPs along analogous lines as the analysis of definite NPs presented in the previous section. In our opinion, an NP can trigger a presupposition in two cases: namely when the determiner is strong or if it is weak but accented. This is formulated in the following NP presupposition scheme. NP PRESUPPOSITION SCHEME Suppose an NP is of the form [DET CN] and C is some context variable. If DET is strong or accented, then the NP triggers the presupposition that the intersection of the respective denotations of C and CN is not empty. The distinction between strong and weak determiners is due to Milsark (1977), and is based on the observation that the latter, but not the former, can occur in postverbal position in there sentences. Thus, for instance, most is a strong determiner, while some is a weak one: (41) a.
* There are most politicians in this hotel.
b. There are some politicians in this hotel. It is worth noticing that no definite NPs are allowed in postverbal there position. For this reason, the phenomenon in (41) is also referred to as the definiteness effect. Partee (1984), De Jong (1987:276) and Zucchi (1995), among others, have argued that all strong NPs trigger an existence presupposition. In certain situations weak NPs can also trigger an existence presupposition, namely when the determiner is accented (van der Sandt p.c.). Consider the following example (small caps indicate stress): (42) If a new teacher is hired, there are NO / FEW girls in this class who immediately have a crush on him. In fact, they are primarily interested in the Backstreet Boys. Here the weak NP NO / FEW girls in this class triggers an existence presupposition. Intuitively, the presupposition is projected and this explains why the pronoun they in the second sentence succeeds in finding an antecedent, thereby referring to the set of girls in this class. Summarizing: the NP presupposition scheme leads to a generalization of the DRT construction rule for definite descriptions in section 4.2, applying to all NPs of the form DET CN where the DET is strong or accented.
23
DET CN Rule, for DET = strong or DET = weak but accented Upon encountering an S of the form , or a VP of the form , where is of the form DET CN[ sg] and DET is either strong or weak but accented, replace S or VP with the following presuppositional DRS and duplex condition, where y and z are fresh discourse referents and C is a fresh context variable.
?@ ? @@ ? DET @@ y ? @??
y CN (y ) C
@
y
C; z C
CN (z)
Note that NPs with a determiner that is either strong or accented (or both) can give rise to the expected partial match ambiguities. Consider the following example: (43) a.
If the new teacher lectures some pupils, most girls immediately have a crush on him.
b. If the new teacher lectures some pupils, at least THREE girls immediately have a crush on him. The respective DRSs for (43.a) and (43.b) are structurally similar: both have a presuppositional DRS in the consequent presupposing the existence of a group of girls. There are two potential antecedents for this presupposition in the antecedent of which the new teacher is ruled out on the basis of number. If we assume that there is no relevant hearer knowledge, then there will be no full match 6 ;. between girls and pupils. However, there will be an H-model M in which [ girl] M \ [ pupil] M = In other words: our modified algorithm predicts that the examples in (43) display a partial match, and a genuine ambiguity between a binding and an accommodation reading is predicted. The binding reading for (43.a/b) can be paraphrased as (44). (44) If thei new teacher lectures somej pupils, there is a group of girlsk among themj and fmost / at least threeg of themk have a crush on himi . When we accommodate the presuppositional DRS in van der Sandtian style, this yields a DRS paraphrasable as (45). (45) There is a group of girlsk and if thei new teacher lectures somej pupils, fmost / at least threeg of themk have a crush on himi . These predictions accord well with our intuitions.
5
D ISCUSSION
In this discussion section a number of issues for future research are mentioned (section 5.1), and a comparison is made with van Deemter’s approach to generalized anaphora (section 5.2).
5.1 Future research We have opted for a frog’s perspective in modifying van der Sandt’s algorithm: that is, we have first worked out the details for definite descriptions, and subsequently argued that the same analysis 24
carries over to NPs in general. Van der Sandt (1992) takes a bird’s eye perspective: his approach is explicitly aimed at all presuppositions, and two of the three examples he gives of partial matches involve non-NP presuppositions, viz. (12.b) and (12.c) repeated below. (46) a.
If John murdered his wife, he will be glad that she is dead.
b. If someone at the conference solved the problem, it was John who solved it. Intuitively, it is clear why these two sentences display a partial match ambiguity. In (46.a) the verb be glad that triggers a presupposition that John’s wife is dead. Since ‘being murdered’ is more informative than ‘being dead’, this would be a partial match of type I. However, various problems present themselves. The consequent contains a propositional presupposition triggered by glad to the effect that John’s wife is dead. If such propositional presuppositions are anaphoric (which, according to some people, they are not, see e.g., Zeevat 1992:396ff), then they refer to other propositions. This would require an extension of DRT to include discourse markers for propositions (maybe along the lines of Asher 1993). How this is to be done, and what the consequences are for the modified resolution algorithm are important questions for future research. In section 3 we noted that presuppositions may but need not be bound in situ. The definition of BINDing given in section 4.2 does not do full justice to this, as it leaves the bound presupposition always in situ. We feel that in many cases the in situ interpretation is the most preferred binding reading.12 However, this is not to say that other binding interpretations are necessarily unavailable (see e.g., (23)). Strand (1997) allows the binding site to be either the source DRS or the target DRS, or one of the sub-DRS sandwiched between these two extremes. While we think that this is an interesting line to pursue, it also raises a number of questions. To name but one, given the variety of non-equivalent binding readings which become available in this way, which is the most preferred one? We do not have clear intuitions on this issue. To clarify it, the distinction between presupposed and asserted information needs to be taken more seriously than we have done in this article.13 In the mean time, we propose to stick to definition 2.
5.2 Van Deemter: generalization of anaphora The revised theory proposed here has much in common with the proposal in van Deemter (1992). In particular, both theories take a DRT-based approach to anaphora and extend it to cover the context dependent interpretation of NPs of all major syntactic/semantic categories. Also, both theories use Westerst˚ahl-style context sets as one of their basic mechanisms. Yet, there are a number of vital differences, most of which derive directly from the work of van der Sandt. A relatively superficial difference lies in the fact that the present proposal is embedded in Kamp & Reyle’s theory of plurals, rather than in that of van Eijck (1983). Another nontrivial difference between the 12 The situation is more difficult when presuppositions interact with intensional operators like might or believe. Sometimes presuppositions appear to be bound outside the scope of an intensional operator. Consider If John has children, his mother believes that he’ll spoil the little bastards. In our opinion, the preferred reading of this sentence is If John has children, they’ll be little bastards and his mother believes that he’ll spoil them (and not, as van der Sandt (1992) predicts, If John has children and they are little bastards, his mother believes that he’ll spoil them). We think that the preferred reading of the sentence comes about via a de re construction of the presupposition trigger with respect to believe and that this presupposition is subsequently bound in situ. There is also a de dicto reading, but somehow this reading is less preferred for the current example, probably because the description the little bastards is the ‘responsibility’ of the speaker (in the sense of Quine-Kaplan-Lewis). Heim (1992) argues that for each presupposition trigger, a de re reading is always preferred over a de dicto reading, but in our opinion this is too strong a claim. We think that, at least for the presupposition triggers under discussion here, there is a systematic de re/de dicto ambiguity, where other factors (plausibility, world knowledge, ‘who is responsible for which description’) may sometimes indicate a preference for one or the other. 13 See Geurts and van der Sandt (1997) for a similar plea. Krahmer (1996, 1998) offers a version of the presuppositions-as-anaphors approach in which presuppositions remain presuppositional after resolution.
25
present account and that in van Deemter (1992) lies in the use of the Milsark-Partee perspective on weak/accented DETs, which allows us to treat non-definite NPs in the same way as definite NPs. A much more substantial difference, however, lies in the fact that we use van der Sandt’s unresolved representations (plus, of course, a version of his resolution mechanism) to make predictions about interpretive preferences. Context variables play an essential role in the present account. In van Deemter (1992), it was assumed, for simplicity, that a given NP could take any suitable and accessible reference marker as its anaphoric antecedent. The choice between possible antecedents, and the choice between an anaphoric or a non-anaphoric interpretation, was not modeled by the theory. Instead, it gave a set of possible interpretations, all except one of which involved Westerst˚ahl-style restricted quantification. In the account of the present article, by contrast, two stages can be distinguished. The first stage results in an unresolved (i.e., underspecified) representation, containing unresolved context variables (i.e., context variables that have not yet been equated to the domain of discourse or some previously-established reference marker). The second stage delivers a partially-ordered set of possible interpretations resulting from the different possible resolutions of the context variables, subject to the new rules governing interpretive preferences. Throughout this article we encountered various other factors which may cause interpretations to be ruled out, including, continuations, the IAH, hearer knowledge, and (de-)accenting. Our understanding of the interpretive preferences predicted by the presuppositions-as-anaphors theory is that these preferences serve to choose among those interpretations that remain when these other factors have done their constraining work.
6
C ONCLUSION
Let us take stock. One way of looking at our present endeavor is as a reconstruction of van der Sandt’s theory of presuppositions. However, as stated in the introduction we think of this exercise as part of a wider research programma on the context-sensitivity of interpretation, in the spirit of Westerst˚ahl (1985), Partee (1984, 1987) and many others. We have primarily been concerned with the context-sensitive interpretation of noun phrases. Our approach rests on the assumption that every NP can be dependent on the linguistic context for its interpretation. Two complicating factors are (i) that often the dependency relation between a would-be anaphor and a would-be antecedent is partial, and (ii) that the relation is by no means unrestricted. We have discussed a number of these restricting factors, in particular (de-)accenting, hearer knowledge and the Informative Anaphors Hypothesis (the IAH). We argued that the presuppositions-as-anaphors theory of van der Sandt (1992) provides an excellent starting point for the current exercise. Beaver (1995:61-62), discussing some problems related to the partial match phenomenon, supposes that these problems will be solved when the theory matures.14 We indeed think that the problems with partial matches can be solved by refining and extending van der Sandt’s algorithm, and we have tried to offer such a refinement. The resulting version of the presuppositions-as-anaphors theory differs from the original proposal (van der Sandt 1992) mainly in the following respects: (1) The new version contains a precise definition of the ‘partial match’ phenomenon; (2) we have modified the resolution algorithm in such a way that — in accordance with van der Sandt’s intuitions — partial match sentences come out as genuine ambiguities; and (3) binding is redefined in such a way that non-identity anaphors receive adequate interpretations. After our exposition of the revised theory we have shown how it may be generalized to account for context-dependent interpretations of other classes of NPs than those discussed by van der Sandt. 14
In fact, we think that Beaver’s examples are not problematic for van der Sandt theory as such. The phenomena discussed by Beaver (an example is (16.b)) all fall in category IV (anaphor is more ‘informative’ than antecedent), and we have seen that these are often marked for independent reasons.
26
Acknowledgements Earlier versions of this work were presented at ‘De Dag’/the workshop on definites (Groningen, November 1996), the DIP colloquium (Amsterdam, March 1997), and the Eleventh Amsterdam Colloquium (December 1997). We thank the audiences on these various occasions as well as David Beaver, Paul Dekker, Bart Geurts, Barbara Partee, Paul Piwek, Rob van der Sandt, Remko Scha, Mari¨et Theune and the reviewers for discussion, comments and suggestions. As always, we alone are responsible for all errors in this article. EMIEL KRAHMER
IPO, Center for Research on User-System Interaction Eindhoven University of Technology P.O.Box 513, NL 5600 MB Eindhoven, The Netherlands e-mail:
[email protected] url: http://www.tue.nl/ipo/people/krahmer KEES VAN DEEMTER
Information Technology Research Institute (ITRI) University of Brighton Lewes Road, Brighton, BN2 4GJ, UK e-mail:
[email protected] url: http://www.itri.brighton.ac.uk/ Kees.van.Deemter/
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